Net Change Theorem and Applications of Integrals

in MES Science3 months ago (edited)

In this video I go through what the net change theorem is and basically illustrate how this concept and the idea of integrals can be applied to any real world application that involves a known rate of change in which a net change is desired. Such an application involves filling a reservoir with water at a know rate and determining the net change in the reservoir volume. In the video I also go through an example explaining the difference between the displacement or net change of the position of a moving object with the total distance it travels.


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Applications of Integrals

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The Net Change Theorem

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This principle can be applied to all of the rates of changes in natural and social sciences.

Here are few examples:

Volume of water in a reservoir at time t:

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Concentration of the product of chemical reaction at time t:

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Mass of a rod of varying density

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Rate of growth of a population n

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Cost of producing x units

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Position of an object moving in a straight line

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Velocity change of the object:

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Example

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